It's just one of those things which I like to call 'ascended fanon', ie it's a fan theory which has taken on a life of its own and been
effectively accepted as a viable and official part of the universe despite there being no direct evidence for it in any screen incarnation, while there being nothing to contradict it either.
Even if it had been thrown around in fan circles before-hand, I think it was the Okuda's
Star Trek Chronology that fed the flames on the blond lab technician being Carol Marcus (as it so often did with this kind of fanon..... note that so many entries in that book are labelled as being "Conjecture", but because of the weight of the Okuda's involvement in Trek at the time, many of us accepted these 'fan theories' in the absence of anything more official being established on-screen).
There are a lot of things regarding TOS that are in fact 'fanon' in this regard. Some of them have subsequently become facts established on-screen, while still others never have, but are, for lack of anything else, "accepted" by the fandom as a kind of 'second tier' continuity anyway.